- Introduction to differential equations
- Order of a differential equation
- Linear Vs Non-Linear differential equations
- Examples of linear and non-linear differential equations

- Classification based on homogeneity
- Discussion about the solutions of a differential equation I
- Discussion about the solutions-part II
- Initial value problems and Boundary value problems
- What is a continuous function?
- Existence and Uniqueness theorem for first order ODEs
- Explicit Vs Implicit Solutions of a differential equation
- Family of solutions

- Slope field introduction
- Finding solution curves on a slope field
- Analyzing a slope field
- Autonomous differential equations
- Equilibrium Solutions
- Stability analysis of a slope field
- Separable differential equations
- Theory behind separation of variables
- Separation of Variables-Solved examples-1
- Separation of Variables-Solved examples-2
- Separation of Variables-Solved examples-3
- Separation of Variables-Solved examples-4

- The standard form a linear differential equation
- Linear equation - integrating factor method development
- Linear equations step by step example solved slowly
- Linear equations many examples solved
- Linear equations hard examples solved

- Introduction to models - Newton's law of cooling
- Newton's law of cooling - video 2
- Half-life
- Carbon dating
- Electrical circuits introduction
- Analyzing circuits
- Mixing Problems
- Falling bodies
- Logistic growth introduction
- Logistic growth solution
- Logistic growth example
- Draining a tank
- Mixing problems 1
- Mixing problems 2

- Preparation for the lesson
- Existence and uniqueness theorem for higher order differential equations
- Existence and uniqueness theorem examples
- Boundary value problems
- Linear independence Vs Linear dependence
- Examples of linear independence and dependence
- Wronskian
- Higher order- Homogeneous Equations
- The fundamental set of solutions
- Non-homogeneous equations

- Introduction to auxiliary equations-Lesson-1
- Distinct Roots case-Lesson-2
- Repeated roots case-Lesson-3
- Complex roots case-Lesson-4
- Higher order differential equations-Lesson-5

- Introduction to method of undetermined coefficients-Lesson-1
- Case 1-First examples in method of undetermined coefficients-Lesson-2
- General overview of how to find the trial form-method of undetermined coefficients-Lesson-3
- Case 2- Overlap- method of undetermined coefficients - Lesson- 4
- Superposition Case - method of undetermined coefficients-Lesson-5
- Higher order differential equations- method of undetermined coefficients-Lesson-6
- Algebra skills needed in method of undetermined coefficients -Lesson-7
- Example 1 - method of undetermined coefficients -Lesson-8
- Example 2 - method of undetermined coefficients -Lesson-9
- Example 3-IVP - method of undetermined coefficients -Lesson-10
- Special Example - method of undetermined coefficients -Lesson-11
- Example 5 - method of undetermined coefficients -Lesson-12

- Variation of parameters - Lesson-1
- Variation of parameters- Methodology - Lesson-2
- Variation of parameters- Example -1 - Lesson-3
- Variation of parameters- Example-2- Lesson-4
- Variation of parameters- Example-3 - Lesson-5
- Variation of parameters- Example-4 - Lesson-6

- Mechanical Vibrations start-Lesson-1
- Mechanical Vibrations-Lesson-2-Free undamped motion
- Mechanical Vibrations-Lesson-3-Example free undamped motion
- Mechanical Vibrations-Lesson-4-free damped motion
- Mechanical Vibrations-Lesson-5-Overdamped motion
- Mechanical Vibrations-Lesson-6-Critically damped motion
- Mechanical Vibrations-Lesson-7-Underdamped motion
- Mechanical Vibrations-Lesson-8-Forced response example 1
- Mechanical Vibrations-Lesson-9-Forced response example 2
- Mechanical Vibrations-Lesson-10-Undamped forced motion with different frequencies
- Mechanical Vibrations-Lesson-11-Resonance

- Introduction to system of differential equations-Lesson-1
- Matrix Form -Lesson-2
- Solutions of a system--Lesson-3
- Linear independence--Lesson-4
- Fundamental set of solutions--Lesson-5
- Nonhomogeneous systems-Lesson-6

- System of differential equations with distinct eigenvalues - Prep-Polynomial Long Division- Lesson-1
- System of differential equations with distinct eigenvalues - Prep-Cubic polynomial factor- Lesson-2
- System of differential equations with distinct eigenvalues - Prep-Determinant of a matrix- Lesson-3
- System of differential equations with distinct eigenvalues - Prep-Gaussian Elimination- Lesson-4
- System of differential equations with distinct eigenvalues - Prep-Gaussian Elimination II- Lesson-5
- System of differential equations with distinct eigenvalues - Introduction- Lesson-6
- System of differential equations with distinct eigenvalues - Eigenvectors of 2 by 2 system- Lesson-7
- System of differential equations with distinct eigenvalues - Eigenvalues of 3 by 3 system- Lesson-8
- System of differential equations with distinct eigenvalues -Eigenvectors of 3 by 3 system- Lesson-9
- System of differential equations with distinct eigenvalues - Homogeneous system- Lesson-10
- System of differential equations with distinct eigenvalues - Example -1- Lesson-11
- System of differential equations with distinct eigenvalues - Example -2- Lesson-12
- System of differential equations with distinct eigenvalues - Example -3- Lesson-13
- System of differential equations with distinct eigenvalues - Example -4 part-1- Lesson-14
- System of differential equations with distinct eigenvalues - Example -3-part-2- Lesson-15
- System of differential equations with distinct eigenvalues - Phase portraits introduction- Lesson-16
- Phase Portraits-Case 1- both eigenvalues are positive- Lesson-17
- Phase Portraits - Case 2 -when both eigenvalues are negative- Lesson-18
- Phase Portraits - Case 3 -when eigenvalues signs are mixed- Lesson-19
- Using an Initial condition in a system of differential equations

- System of differential equations with repeated eigenvalues - Introduction- Lesson-1
- System of differential equations with repeated eigenvalues - Case-1- Eigenvectors- Lesson-2
- System of differential equations with repeated eigenvalues - case-1-writing general sol- Lesson-3
- System of differential equations with repeated eigenvalues - Example-2 Lesson-4
- System of differential equations with repeated eigenvalues - Case-2- Introduction- Lesson-5
- System of differential equations with repeated eigenvalues -Case-2-example-2- Lesson-6
- System of differential equations with repeated eigenvalues -Case-2-3 by 3 example-- Lesson-7
- System of differential equations with repeated eigenvalues - 3 times repeated eigenvalue- Lesson-8
- System of differential equations with repeated eigenvalues -Phase portrait- Lesson-9

- System of differential equations with complex eigenvalues - Preparation- Lesson-1
- System of differential equations with complex eigenvalues - Finding eigenvalues and vectors-Lesson 2
- System of differential equations with complex eigenvalues -Writing the general solution- Lesson-3
- System of differential equations with complex eigenvalues - Identity explained- Lesson-4
- System of differential equations with complex eigenvalues - Example- Lesson-5
- System of differential equations with complex eigenvalues - Phase portraits- Lesson-6

- Non homogeneous system of differential equations -Method of undetermined coefficients- Lesson-1
- Non homogeneous system of differential equations -Method of undetermined coefficients - Lesson-2
- Non homogeneous system of differential equations -Method of undetermined coefficients- Lesson-3
- Non homogeneous system of differential equations -Method of undetermined coefficients- Lesson-4
- Non homogeneous system of differential equations -The fundamental matrix- Lesson-5
- Non homogeneous system of differential equations -Variation of parameters- Lesson-6
- Non homogeneous system of differential equations -Variation of parameters example-1- Lesson-7
- Non homogeneous system of differential equations -Variation of parameters example-2- Lesson-8

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